It should also show up on the game. I haven't had a draw offer in a while so I can't recall the exact mechanism. It may be a pop-up when you first open the game but I'm not sure.
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So when someone in chess.com offers a draw, the offer shows up in my email? Why not the board screen and you can accept the offer there. The email does not offer the option of accepting or rejecting the offer. Am I missing something?